Linear Regression & Population Predictions
Steps of lesson:
1. Warm-up Activity: Ask students to estimate the population for the following areas
 United States - 318,892,103 (July 2014 est.)
 Atlanta 4,715,000 (2012 est.)
 Chicago 9,121,000 (2012 est.)
 Los Angeles 14,900,000 (2012 est.)
 Miami 5,582,000 (2012 est.)
 New York City 20,464,000 (2012 est.)
2. After discussing population as a class, students will predict the population for various global
cities. The cities are listed on the student handout. Students are to record their predictions
before researching population data.
3. Monitor student progress in locating population data.
4. After data is retrieved and organized, students will write a linear regression equation that
compares predicted population to actual population. Students should have previous
experience in writing linear regression equations as well as understanding the components to
the equation.
5. Teacher Notes: Guide students to graph their regression equation and y = x on the same
coordinate plane and to compare the equations. If a student consistently guessed the
population correctly, the equation would be y = x. If their line is below y = x, then they over
predicted population, if it is above, then they under predicted population. Likewise, if the
slope of the line is less than 1, then the populations were over predicted and if the slope is
greater than 1, then were under predicted. Compare the slopes of student equations to
determine whose slope is closest to one. The student that has the slope closest to one is the
best predictor. See the answer key for graphical displays.
Extension:
 Student may interview their parent and ask him or her to predict population for the same
global cities. Then students can write a regression equation for their parent and compare
their predicting abilities to their parent.
 Students may locate the global cities on a map.

The North Carolina Geographic Alliance http://geo.appstate.edu/NCGA
Linear Regression & Population Predictions
1. Predict populations for the following cities. Record your results in the chart
below.
City/Town
Predicted
Population (x)
Actual Population
(y)
Beijing, China
Cairo, Egypt
Delhi, India
London, United
Kingdom
Mexico City,
Mexico
Moscow, Russia
Paris, France
Seoul, South Korea
Tokyo, Japan
2. Find the actual population for the cities listed in the chart. Record your results in the
chart above.
3. Write a regression equation comparing the predicted population to the actual
population. Round slope and y – intercept 4 decimal places.
4. What would the equation be if you predicted the population for each city correctly?
Compare your results to this equation.

The North Carolina Geographic Alliance http://geo.appstate.edu/NCGA
Linear Regression & Population Predictions
ANSWER KEY: Population Predictions
Predict populations for the following cities. Record your results in the chart below.
City/Town
Predicted
Population (x)
Beijing, China
Cairo, Egypt
Delhi, India
London, United
Kingdom
Mexico City,
Mexico
Moscow, Russia
Paris, France
Seoul, South Korea
Tokyo, Japan
Actual Population
(y)
17,311,000
17,816,000
22,242,000
8,586,000
19,463,000
15,512,000
10,755,000
22,547,000
37,126,000
Examples of Scatter Plots compared to y = x.
a) Underestimating: The actual population is greater than the predicted,
therefore the student underestimated.
Actual
Population
Predicted Population
b) Overestimating: The actual population is less than the predicted, therefore the
student overestimated.
Actual
Population
Predicted Population
Sources: US Census, World Atlas

The North Carolina Geographic Alliance http://geo.appstate.edu/NCGA